FP1 dividing complex numbers

for something like

$\dfrac{3-5i}{2i}$

why not multiply by 2i why multiply by -2i instead?

for something like

$\dfrac{3-5i}{2i}$

why not multiply by 2i/2i why multiply by -2i/-2i instead?

for something like

$\dfrac{3-5i}{2i}$

why not multiply by 2i/2i why multiply by -2i/-2i instead?

While the conjugate of 2i is -2i, it is not necessary. As you've suggested you can multiply by $\dfrac{2i}{2i}=1$

But where the complex number in the denominator has both a real an imaginary part, you multiply by the conjugate which is $a-bi$ for a complex number $a+bi$) as you make use of the difference of two squares ($a^2-b^2=(a-b)(a+b) \Rightarrow (a-bi)(a+bi)=a^2-(bi)^2=a^2+b^2$).
This makes the denominator real and is similar to rationalizing the denominator with surds.

Because -2i is the conjugate. Remember the conjugate of a+bi is a-bi

You can if you want to, infact, I'd skip the 2's and multiply by $\frac{i}{i}$ myself. The importance of keeping the $-bi$ in other examples is as KTA's answer.

so am i trying to get rid of the i on the bottom or is it something else i'm trying to get rid of or change

You just want to get rid of the $i's$ at the bottom so your final complex number is of the form $x + iy$.

Yes because conjugates get rid off the imaginary parts. But as Zacken said, you can just multiply by i/i because the denominator has no real part to it. If the denominator is in the form a+bi where a and b =\= 0 then you need to multiply the numerator and denominator by the conjugate and multiplying them only by i won't get rid off the imaginary part in the denominator. Just treat these in the same way as rationalising the denominator with surfs

Are you learning FP1 and are you in year 11, going into year 12?


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eyy old threads
i'm in year year 12 going to 13

Old threads ?

Oh right, so are you doing Further Maths AS?

1 day old

No i should've done it but i didn't take it

Oh right xD. Anyway, enjoy! I'm at the same stage, so let's collaborate on questions instead of asking directly on threads (because I practically do the same thing)?


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right i'm learning from new, so currently i've gone through(supposedly) the first chapter of complex numbers, i made another thread on it xD

Don't worry, I've finished chapter 3. We are both learning from new. I've forgot a bit of chapter 1 so I will go back. I've forgot chapter 2 I think lol and chapter 3 was just ****ing hard (a bit)


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